How can I simply map a procedural gradient from the equator to the poles of a sphere?
Here is my result:



And here is my node setup:



The absolute value node works well here because instead of going from a large negative to a large positive, with zero in the middle (creating a standard linear gradient), we instead achieve a positive value on both the top and bottom of the sphere, with it linearly going towards 0 in the middle.

You can change the color ramp type to 'ease' to get a larger area of black in the middle if you want, and changing the emission value also affects it.